In the design of insulating wall and sound-reproducing system, the scoustic power of sound source and the required power for audio device are fundamental data to determine the specification. To obtain the reference data fitting to this purpose, acoustic power of orchestra music was investigated, since it is typical and generates the largest peak power among common renditions in auditorium. There are many theoretical sound-field equations proposed for the measurement of the sound source power with its relation to the sound pressure at a distance from the source, however, their applications are limited to the case of a nondirectional sound souce. To simulate wide arrangement of orchestra instruments and then to approximate sound pressure with the measurement of an orchestra, a model of orchestra was composed of fine nondirectional sound sources as shown in Fig. 2. Using this model, powers of orchestras will be estimated later. In this paper, firstly, the experimental verification of the theoretical sound field given by Eq. (6) for a single nondirectional sound source is shown in Figs. 3, 4, 5. The sound field Eq. (6) was derived from the view point of geometrical acoustics: The summation was carried out for all incident sounds to the receiving point prescribed by the law of geometrical reflection up to the upper bound term k, which is indirectly given by ub, the ratio of partial sum for k-1 terms to that for k terms in Eq. (6). From other consideration, it was found that ub=0. 99 is practically large enongh to obtain precise sound pressure by Eq. (6). In the region of high frequency, absorption of sound in air was taken into account and theoretical sound pressure was calculated with the absorption coefficient m=10^<-3> to get good agreement with measured sound pressure level shown by dots in Fig. 5. Secondly, the total sound pressure produced by spatially distributed sound sources that simulate orchestra instruments in the assembly was examined by comparing theoretical results with measured ones. Both computed and measured results in Fig. 6 were obtained under the condition that each sound source radiated equal power noise consisting of three half-octave-band noises whose outputs followed mean orchestra spectrum. Since another good conformity between these two sound fields is seen in Fig. 6, Eq. (6) is believed sintable for the evaluation of the power of distributed sound sources as well. Thirdly, to prove the validity of these distributed sound sources as an orchestral model, the measured rms sound pressures of an orchestra music were compared with the sound field by Eq. (6) and a good agreement between them was obtained as shown in Fig. 7. It should be noted that to attain the same uni-directivity condition when the orchestra music was picked up, the correction procedure from non to uni-directivity depicted in Fig. 7 was applied in advance to the theoretical sound field that is computed under the condition of nondirectivity. Lastly, the follwing acoustic power of an orchestra is obtained by applying Eq. (6) to the orchestra model. P. I. TCHAIKOVSKY'S SYMPHONY NO. 6 (69-piece orchestra) MEAN 16mW PEAK 13W. If acoustic and geometrical conditions of hall and relative location of orchestra to microphone are assumed the same, acoustic powers of other orchestras will be estimated in the similar way referring to the sound pressures given in the literature below. For example, M. RAVEL'S BOLERO (107-piece orchestra) MEAN 83mW PEAK 52W. S. Ehara: "Instantaneous Pressure Distributions of Orchestra Sounds, " J. A. S. J. , Vol. 22, No. 5 (Sept. 1966) pp. 276-289.
So far, the tone quality of electronic musical instruments have been considered as "artificial" and "unfamiliar", when compared with those of natural musical instruments, and it has been expected that there is an essential difference between them. The primary reason for such a difference is the fact that the electronic musical instruments today are manufactured considering only physical properties such as spectral structure of sound, attack time and so on, but overlooking the other physical properties of general musical tones as shown in Fig. 1. Here, the authors carried out two sets of psycho-acoustical experiments to explain the difference in tone quality more concretely, through the introduction of the concept "naturalness" of musical tone. The purpose of the first experiment is to propose a definition of the concept of "naturalness". As shown in Table 2, several kinds of tones representing timbres of string, wind, and reed families were selected. Fifteen subjects rated the tones on each of scales by the category method. From the matrix of rating scores for each timbre, the correlation matrices were calculated and analyzed by the principal axis method. The axis corresponding to the naturalness was explained by two or three psychological rating scales. These psychological rating scales suggest the existence of similar structure in the concept of naturalness for the three timbres. In the second experiment, the influence of "inharmonicity" of partial tones on the tone quality of musical tones was studied, applying concept of naturalness defined in the first experiment. The sound stimulus was synthesized by a sound synthesizer. This device has oscillators for four sounds of 349, 392, 440 and 466Hz and the frequency of the partial tones of each sound can be modulated up to the 15th independently at 6 steps (21, 14, 7, 0, -7, -14 cent). In the first part of the experiment, about 100 sounds of various kinds, whose frequency structurs are illustrated in Table 3 for each of the four timbres, were prepared by this device. Then psychological difference in tone quality between the sound whose partial tones are all in harmonic relations to the fundamental tone, and the sound whose partial tones are in inharmonic relations, is scaled. According to the variance analysis, the degree of effective partial tones, whose inharmonicity contributes to the psychological difference in tone quality was determined. Referring to the results of variance analysis, an experimental formula for the psychological difference R in tone quality in terms of physical variables was derived as follows. R=αΣKn|log(fn/fsn)|, where fn: frequency of the nth degree non-integral partial tone of fundamental tone, fsn: frequency of the nth degree integral partial tone of fundamental tone, Kn: weight coefficient of the nth degree partial tone. Fig. 8 through 11 give the diagrams showing the correlation between the experimental and theoretical values for each timbre. We can deduce the aspects of psychological variation in tone quality from the physical variables, when the partial tone is modified in an inharmonic relation. Fig. 12 shows the relation between the naturalness and the sound with inharmonic partial tones. On this basis, we can infer that an adequate amount of inharmonicity in the partial tones increases the naturalness, while an excessive inharmonicity reduces the naturalness, maximun naturalness being obtained for R at about 10 for each timbre.
This paper deals with the analysis on the resonant frequencies of the H-type transeversely vibrating resonator suitable for low frequency below about 10kHz. A tuning-fork and a transeversely vibrating thin bar have been used, up to the present, as the resonator for frequency below about 10kHz. The resonant modes of the resonator are constant regardless to the dimentions at the time of inherent resonance. On the other hand, the modes of the H-type resonator described in this paper are dependent upon the dimensions of the resonator. Since such resonator as that having various resonant mode at inherent resonance has not been put in practical use until now, H-type resonator having different resonant modes is proposed in this paper to be practicaly. From the view point of practicability of H-type resonator, the resonant frequencies are analyzed as a function of the dimensions of the resonator. In the second chapter, the first mode vibration of the H-type resonator made of a thin steel sheet (Fig. 1) is analyzed from the analogy of the network (Fig. 2) equivalent to the transeversely vibrating mechanical system, and the convenient diagrams for design of the H-type resonator (Figs. 3, 4) and the optimal dimension to reduce the size of the resonator under the condition of constant area of the resonator are given. Furthermore, difference between the H-type resonator and a tuning-fork or a transversely vibrating bar aise made clear. (Fig. 7) The resonant modes are shown, as a fuction of the dimension of the resonator. (Fig. 6) The detailed analytical process of the vibraion modes of the resonator is given in the appendix. (Figs. A-1, A-2) Because the error of the resonant frequencies obtained from the design diagrams to measured ones is less than several percents in case of usual dimension(Fig. 4), it is proved that the design programs presented in this paper can be said to fit practical purpose. In the third chapter, as for the step-shaped H-type resonator of small size applicable to lower frequency range (Fig. 8), the result of the analysis is stated on the resonant frequency. (Figs. 9, 10) Even in this case, the calculated value of resonant frequency is nearly equal to the measured one. In the forth chapter, from the standpoint of the application of the H-type resonator as multi-mode vibrator (Figs. 12, 13), the condition imposed to the dimension is obtained that resonant frequency of the transverse vibration perpendicular to the frame-work agrees with that in the frame-work plane. (Figs. 15, 16) The multi-mode resonators can be constructed by chamfering the H-type resonator of the dimension making the resonant frequencies of the both mode mentioned above agree with each other.